What is the best approach to modeling a non-human character with an obscure/disproportionate anatomy?
I suggest using sculpting with dynamic topology. It is perfect for extruding tentacles, ears and horns.



Also available are extrusion in edit mode. Select a quad and hit e. Drag out a bit, move and rotate and continue extruding to form your limb. Apply subdivision to get a smooth surface (2 or 3 steps maybe).



With subdivision modifier: